Orientation dependence of the acoustic backscatter for elongated zooplankton

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Abstract

The width of the main lobe of the acoustic backscatter directivity pattern of decapod shrimp
(Palaemonetes vulgaris) is examined versus acoustic frequency. Using the distorted wave
Born approximation (DWBA) and the geometry of a prolate spheroid, an analytic formula
for the backscatter cross section as a function of orientation angle is derived. A directivity
pattern is determined from the analytic formula and the width of the main lobe (beam width)
is computed. The relationship between beamwidth and acoustic frequency is presented in
plots of beamwidth versus ka and L/λ. The model is adapted to experimental limitations of
animal motion, discrete sampling and observed side lobe levels. The backscatter directivity
patterns of live decapod shrimp, determined experimentally at frequencies between 72 and
525kHz, are presented. A non-monotonic relationship between beamwidth and frequency
is illustrated in this study. This relationship is in contrast to the monotonic relationship
exhibited when sound scatters off of an impenetrable flat plate. Reasonable agreement is
found between the theoretically predicted beamwidths and most experimental data, where
the beamwidth was more-or-less oscillatory about a mean value of 19°. The structure can at
least be partly explained by scattering theory.

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Submitted in partial fulfillment of the requirements for the degree of Ocean Engineer at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 1993

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